an equation in slope intercept form for the line that passes through (5,7) and is parallel to the line y=4/5x-6

Answer 1

The problem gives the formula for the first line in slope-intercept form: y=4/5x-6

The slope of that line is m=4/5 [y=mx+b where m=slope and b=y-intercept]

All parallel lines have the same slope, so the parallel line has the formula: y = (4/5)x + b

Use the point (5,7) to find the value of b:

7 = (4/5)(5) + b

7 - 4 = b

3 = b

The formula for the line is: y = (4/5)x + 3

Answer 2

Parallel to the line y = 4/5x - 6 means it has the same slope as y = 4/5x - 6. The slope of that line is 4/5 (it's the coefficient in front of the "x").

You can use the point-slope form ( y - y₁ = m(x - x₁) where "m" is the slope and (x₁, y₁) is a point on the line) to get the equation and then manipulate it into the slope intercept form (y = mx + b where "m" is the slope and "b" is the y-intercept).

So plugging in m = 4/5 and (x₁, y₁) is (5, 7):

y - 7 = 4/5(x - 5)

y - 7 = 4/5x - 4

y = 4/5x + 3

Answer 3

line y = 4/5x - 6 is in form y = mx + b, where m is slope, so slope of that line is 4/5

line parallel to that line will have same slope 4/5

equation of line going through 5,7 with slope 4/5 in point-slope form: y - y1 = m(x - x1) is

y - 7 = 4/5 (x - 5)

use algebra to get into form y = mx + b:

5y - 35 = 4(x-5)

5y - 35 = 4x - 20

5y = 4x + 15

y = 4/5x + 3